In HSDP Access (HSDPA), as well as many other communication systems, there are applications where a binary decision is required but wherein the penalty of error is unequal as between the two decisions.
For example, HSDPA uses an acknowledge/not acknowledge (ACK/NACK) signal where the user equipment (UE) indicates whether or not a transmitted block of data has been successfully decoded. It has been recognized that it is more injurious to system performance for a NACK message to be incorrectly interpreted as an ACK than for an ACK message to be incorrectly decoded as a NACK. In the latter case, the error would result in a transmission block being unnecessarily retransmitted; which amounts to only a small loss in efficiency. In the former case, the transmitting side would assume success for the previously transmitted block, and would not resend it. This is a catastrophic failure, causing serious system disruption.
Several obvious techniques have been recognized to bias the answer in favor of identifying the condition with the NACK. For example, in normal coherent demodulation of binary phase shift keying (BPSK), the output signal is often normalized, e.g., an ideal signal representing 1 is +1.0, while an ideal signal representing 0 would be −1.0 and, in a typical channel, which has impairments, interference and noise, the normalized output may take on any value therebetween.
In an unbiased decision, if an output z>0 then the process declares 1, and, if the output z<0 then the process declares the output=0. In a biased decision, if the output z>X then declare 1, otherwise declare 0. X is identified as the threshold value and is selected based on the analysis. If it is desired to favor the output 1, then X will be negative; e.g., a small negative number; e.g., minus 0.1, etc.
Employing the above process, normalizing the output and deriving the optimum threshold can be delicate and complex to implement and is subject to degradations due to tolerances in the implementation.